Quantum chemical calculations using density functional theory have been carried out for the cyclic (alkyl)(amino)carbene (cAAC) complexes of the group 11 atoms [TM(cAAC)(2)] (TM = Cu, Ag, Au) and their cations [TM(cAAC)(2)](+). The nature of the metal-ligand bonding was investigated with the charge and energy decomposition analysis EDA-NOCV. The calculations show that the TM-C bonds in the charged adducts [TM(cAAC)(2)](+) are significantly longer than in the neutral complexes [TM(cAAC)(2)], but the cations have much higher bond dissociation energies than the neutral molecules. The intrinsic interaction energies ?Eint in [TM(cAAC)(2)](+) take place between TM+ in the S-1 electronic ground state and (cAAC)(2). In contrast, the metal-ligand interactions in [TM(cAAC)(2)] involve the TM atoms in the excited P-1 state yielding strong TM p(pi) -> (cAAC)(2) p backdonation, which is absent in the cations. The calculations suggest that the cAAC ligands in [TM(cAAC)(2)] are stronger p acceptors than s donors. The trends of the intrinsic interaction energies and the bond dissociation energies of the metal-ligand bonds in [TM(cAAC)(2)] and [TM(cAAC)(2)](+) give the order Au > Cu > Ag. Calculations at the nonrelativistic level give weaker TM-C bonds, particularly for the gold complexes. The trend for the bond strength in the neutral and charged adducts without relativistic effects becomes Cu > Ag > Au. The EDA-NOCV calculations suggest that the weaker bonds at the nonrelativistic level are mainly due to stronger Pauli repulsion and weaker orbital interactions. The NBO picture of the C-TM-C bonding situation does not correctly represent the nature of the metal-ligand interactions in [TM(cAAC)(2)].